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Differential Equations question

2021 · 17 Mar · Shift 2 · Q33

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JEE Main
Mathematics
Differential Equations
2021 · 17 Mar · Shift 2 · Q33

Differential Equations question

2021 · 17 Mar · Shift 2 · Q33

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

Let y = y(x) be the solution of the differential equation

\cos x(3\sin x + \cos x + 3)dy = (1 + y\sin x(3\sin x + \cos x + 3))dx,0 \le x \le {\pi \over 2},y(0) = 0

. Then,

y\left( {{\pi \over 3}} \right)

is equal to :

A
$2{\log _e}\left( {{{\sqrt 3 + 7} \over 2}} \right)$
B
$2{\log _e}\left( {{{3\sqrt 3 - 8} \over 4}} \right)$
C
$2{\log _e}\left( {{{2\sqrt 3 + 10} \over {11}}} \right)$
D
$2{\log _e}\left( {{{2\sqrt 3 + 9} \over 6}} \right)$

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